Schrodinger's Bat

Turning the Page

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In response to last week's piece, several readers inquired about the graph of the Detroit Tigers that tracked their performance and Normalized Weighted Age (NWA) since 1980. In particular, the question arose as to whether team age is a leading or a lagging indicator of team performance. In other words, can team age be used as a predictor of success in the near term (a leading indicator), or is it the case that winning percentage tells us something about team age into the future (a lagging indicator)?

A first stab at the answer can be given by calculating the mean NWA for both the previous three years and the subsequent three years. When we do so, what we find is that while both are positively correlated with winning percentage, the previous three years are only barely so, while the subsequent three years that are correlated much more strongly. The following table lists the correlation coefficients (denoted as r, a value that ranges between -1 and 1, and that measures the strength of the linear relationship, with -1 being perfectly negative and 1 being perfectly positive) for various time periods.

The strength of both correlations rose after 1976 and the beginning of the free agent era, as the ability to keep players who are both good and older became essentially a function of payroll. Teams with higher winning percentages can better afford to restock their rosters with older players who perform well. Still, whether before or after the advent of free agency, it is clear that a winning percentage in a particular year tells you more about the relative age of the team in the next three years than the age of the team from the previous three years tells you about winning percentage in a given year. In that respect, anyway, Normalized Weighted Age is a lagging indicator.

We can speculate that this is the case for several reasons. First, teams that perform well are typically loathe to abandon those players who were responsible for that success, and only do so when things totally fall apart or the players retire. Second, teams that are on the cusp of making the postseason or have made it already often attempt to fill the holes they still have with veterans, at the same time that their core players age, and they don't rebuild until it's clear that making the postseason is an improbability.

Does that fully answer the question? It can be argued that it does not, since the average age of a team over several years may in fact have little resemblance to the actual aging curve of the team. One need only examine the Tigers graph from the previous column to note how fast a team can age (1982-1984) and how fast youth can take over (1994-1996).

As a result, we might also ask whether a trend in age in either direction prior to or subsequent to a particular season might tell us something about winning percentage. In other words, does a steady rise or fall in team age portend success or failure on the field, and likewise, does winning percentage correlate with an impending change in team age? By calculating the geometric mean of the percentage increase in NWA for the previous and subsequent three seasons (including the season at hand since team age is largely determined before the season begins) we can put a number to the trend towards increasing or decreasing team age.

For example, the Houston Astros of 1989-1991 recorded the largest three-year average decrease in NWA of -5.2%. In 1988, when they had a record 82-80, they had NWA of 1.09 by giving significant playing time to Nolan Ryan (41), Bob Knepper (34), Mike Scott (33), Buddy Bell (36), and Rafael Ramirez (30). Three years later, they had a NWA of 0.93 in 1991, as they'd reloaded with Andujar Cedeno (23), Luis Gonzalez (25), Jeff Bagwell (25), Darryl Kile (24), and Pete Harnisch (26), and finishing at 65-97. On the flip side, Connie Mack's 1925-1927 Philadelphia A's saw an annualized increase in age of 5.3% while going from a record of 71-81 and a NWA of 0.92 in 1924 to a 91-63 second-place finish and an NWA of 1.07 using such graybeards as Ty Cobb (40) and Jack Quinn (43).

More recently, the Arizona Diamondbacks of 1998-2001 recorded an annualized increase in age of 4.1% as the team went from a record of 65-97 with an NWA of 0.98 in their inaugural 1998 season (including guys like Travis Lee (24), David Dellucci (24), and Brian Anderson (26)) to a record of 92-70 and an NWA of 1.10 in 2001 (with players like Mark Grace (37), Steve Finley (36), and Randy Johnson (36) added to the mix). Although not near the top in the three-year growth trend, the 2006 Royals jumped in age 7.5%, the eighth-highest one-year increase in history, as a byproduct of their additions of Mark Grudzielanek (36), Reggie Sanders (38), and Mark Redman (32). The 2006 Marlins, on the other hand, recorded the single-largest drop in average age, seeing a 12.5% decline by jettisoning Carlos Delgado, Jeff Conine, Paul Lo Duca, and Al Leiter. From a three-year perspective, the Seattle Mariners have come down from an NWA of 1.08 in 2003 (93-69) to just under 0.99 in 2006 (78-84), recording an annual 3.1% decline.

Those examples and the results from the average NWA discussed above should give you a feel for what we see when we correlate the three-year trends with winning percentage. The correlation coefficient for winning percentage and the previous three-year trend comes out weakly positive at 0.26, while the correlation coefficient for the subsequent three-year trend comes out at 0.19. To illustrate the relationship, the following graph shows the scatter plot of the previous three-year trend and winning percentage, along with the trend line represented by the weak correlation.

While the strength of the relationship is pretty weak, we can interpret this result as indicating that the trend in team NWA can be thought of as more a leading rather than a lagging indicator.

But how does this jive with the previous result, where NWA appeared to be a lagging indicator? Essentially, my interpretation is that as teams age, they tend to get better, and once better they tend to plateau briefly, treading water before getting younger and worse in the process.

Given this result, I thought it might be interesting to take a quick look at the National League Central (sans commentary), and how the six teams are trending in terms of NWA and winning percentage. In each graph NWA is on the red line (y-axis on the right) and winning percentage on the blue (y-axis on the left).

A second question that arose concerned the conflating factor of payroll in the comparison of team age and performance. Specifically, are the graphs in the previous article that show a steady increase in winning percentage with an increase in team age really just a reflection of the fact that higher-payroll teams tend to outperform lower payroll teams?

To a large extent, at least in the last 25 years, that is indeed the case. The more reliable payroll data we have to work with only goes back to the late 1980s. Even so, from 1990 through 2006 normalized payroll (the team payroll divided by the average payroll for teams in that season) is correlated very strongly (r of 0.75) with NWA. Given the wide revenue disparity that has opened up in the past 15 years and the structure of the free agency system, one could hardly expect otherwise. Large payroll teams disproportionately employ older players, because they can afford them.

Those older players are on average better than younger players, which leads to normalized payroll being correlated with winning percentage to the tune of 0.42. Since we saw in last week's column that team NWA is correlated with winning percentage at 0.38 (from 1977-2006), we can reasonably conclude that in the most recent era it's payroll that is the driver in determining a team's age, and that with age comes performance on the field.

The underlying question, however, is whether as a roster construction strategy, teams should be actively looking to get older in an effort to boost their record?

This idea is akin to one of Charles Darwin's favorite analogies for describing natural selection. Darwin used an analogy of a wedge in the chapter titled "The Struggle For Existence" contained in The Origin of Species:

In looking at Nature, it is most necessary to keep the foregoing considerations in mind--never to forget that every single organic being around us may be said to be striving to the utmost to increase in numbers; that each lives by a struggle at some period of its life; that heavy destruction inevitably falls either on the young or old, during each generation or at recurrent intervals…The face of Nature may be compared to a yielding surface, with ten thousand sharp wedges packed close together and driven inwards by incessant blows, sometimes one wedge being struck, and then another with greater force.

In an 1856 manuscript (his longer and unpublished version of his theory), Darwin also noted that "sometimes a wedge…driven deeply in forcing out others," the point being that new species (wedges) can often find a niche only by discovering a tiny ecological space between existing species (other wedges) and hammering itself in by forcing another wedge out. In other words, each species entry requires some advantages that allow it to be successful in this wedging process.

Leaving aside the issue as to whether or not natural selection always or even usually follows this model, competition in the baseball world is analogous in that team rosters (the face of Nature, if you will) are packed closely together with players (wedges), and in order to secure a spot, a new player must often "strike a blow" to force an existing wedge out of his spot.

This can be illustrated as in the graph below, where the pink curve represents the number of plate appearances given to players by age, while the green line represents the normalized OPS of all players of that age. Perhaps counter intuitively, while individual performance curves have the characteristic sharper downward appearance as the player reaches his early 30s, the performance curve looks different when drawn for the group as a whole. The selection pressure on older players is intense, so those that survive the "incessant blows" of their younger competitors are therefore necessarily better adapted to survival.

Of course, keep in mind that the green line in the graph represents only offensive value, so when considering overall value by including defense the decline will start a little earlier, as the selection pressure builds for these other, additional reasons. That said, to the extent that teams (read: the Cubs) can afford veteran players and are properly positioned to take advantage, it probably does make sense to add them in an effort to dramatically improve the club.

Riding the Wave of Performance?

The final question that readers were curious about after the previous column was my decision to use NWA to compare to winning percentage rather than incorporating the individual performance curves previously mentioned. To be frank, that idea hadn't even entered my mind, but having been properly provoked I applied the standard curve to all of the 2,136 teams to produce a Percentage of Peak Performance (PPP) indicator for each team. The following table lists the top and bottom 20 teams in terms of PPP.

The 1981 Giants came closest to the Platonic ideal of peak performance at 94.8%, where 100% corresponds to 26 years old (in an effort to simplify I didn't use different curves for hitters and pitchers). On the other hand, the 2005 Yankees--the oldest team in history both in an absolute sense, and relative to their league--were furthest from that ideal at 65.2%. and outdistancing the 1982 Angels.

As you might have expected, the correlation between PPP and winning percentage is a negligible and slightly negative -0.11. This is the case since the individual performance curve does not equate to that for the groups with the result that older teams would be expected to perform more poorly than they actually do. This is also illustrated by the fact that the top and bottom teams have aggregate winning percentages of .448 and .537 respectively.